How do you graph #R(x) = (x + 2)/(x^2  4)#?
The graph would be the graph of
By signing up, you agree to our Terms of Service and Privacy Policy
To graph the function R(x) = (x + 2)/(x^2  4), follow these steps:

Determine the domain of the function by finding the values of x for which the denominator (x^2  4) is equal to zero. In this case, the denominator factors as (x  2)(x + 2), so the function is undefined at x = 2 and x = 2. Therefore, the domain is all real numbers except x = 2 and x = 2.

Find the vertical asymptotes by setting the denominator equal to zero and solving for x. In this case, x^2  4 = 0, which factors as (x  2)(x + 2) = 0. So, the vertical asymptotes are x = 2 and x = 2.

Determine the horizontal asymptote by analyzing the behavior of the function as x approaches positive or negative infinity. In this case, as x approaches positive or negative infinity, the function approaches zero. Therefore, the horizontal asymptote is y = 0.

Find the xintercepts by setting the numerator equal to zero and solving for x. In this case, (x + 2) = 0, so x = 2. Therefore, the xintercept is (2, 0).

Find the yintercept by evaluating the function at x = 0. In this case, R(0) = (0 + 2)/(0^2  4) = 2/(4) = 1/2. Therefore, the yintercept is (0, 1/2).

Plot the vertical asymptotes, horizontal asymptote, xintercept, and yintercept on the coordinate plane.

To determine the behavior of the function between the vertical asymptotes, choose some test points within each interval and evaluate the function at those points. Plot the resulting points on the graph.

Connect the plotted points smoothly to form the graph of R(x) = (x + 2)/(x^2  4).
Note: It may be helpful to use a graphing calculator or software to visualize the graph accurately.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 At the book fair there were 144 students to every 9 teachers. If the amount of teachers to students stayed proportional, how many students would be there if there were only 5 teachers?
 How do you divide #(x^4x^3x^27x7)/(x2) #?
 How do you simplify and restricted value of #((a  4) (a + 3)) / (a^2  a) div( 2 (a  4)) /( (a + 3) (a  1))#?
 How do you divide #(6x^43x^32x^24x7)/(x^2+3) #?
 How do you solve #x^2/ (x^24) = x/(x+2)  2/(2x)#?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7